The absolute magnitudes of RR Lyrae stars from HIPPARCOS parallaxes

Using the method of "reduced parallaxes" for the Halo RR Lyrae stars in the HIPPARCOS catalogue we derive a zero point of 0.77 +/- 0.26 mag for an ass umed slope of 0.18 in the M-V-[Fe/H] relation. This is 0.28 magnitude brigh ter than the value Fernley et al. (1998a) derived by employing the method o f statistical parallax for the identical sample and using the same slope. We point out that a similar difference exists between the "reduced parallax es" method and the statistical parallax method for the Cepheids in the HIPP ARCOS catalogue. We also determine the zero point for the M-K-log P-0 relation, and obtain a value of -1.16 +/- 0.27 mag (for a slope of -2.33). The distance moduli to the HIPPARCOS RR Lyrae stars derived from the two relations agree well. The derived distance scale is in good agreement with the results from the M ain Sequence fitting distances of Galactic globular clusters and with the r esults of theoretical Horizontal Branch models, and implies a distance modu lus to the LMC of 18.61 +/- 0.28 mag.